function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
J =  (-1 * y' * log(sigmoid(X * theta)) - (1 - y') * log(1 - sigmoid(X * theta))) / m;
grad = (X' * (sigmoid(X * theta) - y)) / m;

theta(1) = 0;
J = J + (theta' * theta) * lambda / (2 * m);
grad = grad + lambda * theta / m;

% =============================================================

end
